Can the same input for a plain neural network be used for a convolutional neural network?
There is no restriction on how you input a data to a NN. You can input it in 1D arrays and do element-wise multiplication using 4-5 loops and imposing certain conditions(which will be slow and hence $nD$ matrix notations are used for a CNN).
Ultimately, the library you are using (TensorFlow, NumPy might convert it into its own convenient dimensions).
The main thing different of a CNN from a normal NN is:


The number of parameters of a CNN in a convolutional layer is less than the number of input features.
$parameters \le features$ (in general it is less than). 


Different people have different ways of viewing how the convolutional layer work but the general consensus is that the weights of the convolutional layers of a CNN are like digital filters. It will be a $nD$ filter if input dimension is $nD$. The  output is obtained by superimposing the filter on a certain part of the input and doing element-wise multiplication of the values of filter and the values of the input upon which the filter is superimposed upon. How you implement this particular operation depends on you.

So the answer to your question will be same network cannot be used, but it might be used with modifications (a normal NN is the limiting case of a CNN where $features=parameters$.